[Paper Review] Dynamical mass matrices from moduli fields

Emilian Dudaş|ArXiv.org|Feb 6, 1996

Advanced Algebra and Geometry3 citations

TL;DR

This paper proposes that fermion mass matrices in supergravity-inspired effective field theories arise dynamically from gauge singlet moduli fields, with homogeneous functions of zero degree in moduli generating Yukawa structures analogous to those from U(1) family symmetries. The modular symmetry replaces the need for explicit flavor symmetries, and crucially, flavor-changing neutral currents from soft terms vanish identically at the Planck scale, offering a natural solution to the flavor problem.

ABSTRACT

We review recent work on the structure of the fermion mass matrices in supergravity effective superstrings. They are generally given at low energy by non-trivial functions of the gauge singlet moduli fields. Interesting structures appear in particular if they are homogeneous functions of zero degree in the moduli. In this case we find Yukawa matrices very similar to the ones obtained by imposing a $U(1)$ family symmetry to reproduce the observed hierarchy of masses and mixing angles. The role of the $U(1)$ symmetry is played here by the modular symmetry. The Flavor Changing Neutral Currents effects at the Planck scale coming from the soft terms are identically zero. A dynamical scenario is discussed which allow to generate the observed hierarchies.

Motivation & Objective

• To understand the origin of fermion mass hierarchies and mixing angles in effective field theories derived from superstrings.
• To identify mechanisms in supergravity compactifications that naturally generate the observed pattern of quark and lepton masses.
• To show that modular invariance of the moduli fields can replace the need for explicit U(1) family symmetries in flavor models.
• To demonstrate that flavor-changing neutral currents from soft terms are identically zero at the Planck scale, solving a key flavor problem.
• To propose a dynamical scenario for generating the observed mass hierarchies through moduli-dependent couplings.

Proposed method

• Analyzes the structure of Yukawa couplings in supergravity effective theories as functions of gauge singlet moduli fields.
• Considers the case where these couplings are homogeneous functions of zero degree in the moduli, leading to scale-invariant structures.
• Uses modular symmetry as a replacement for explicit U(1) family symmetries to constrain the form of the mass matrices.
• Derives the soft-breaking terms and shows that their flavor-violating contributions vanish identically at the Planck scale due to the symmetry structure.
• Constructs a dynamical scenario where the vacuum expectation values of moduli fields generate the observed mass hierarchies.
• Applies the framework to the low-energy effective theory, focusing on the structure of the fermion mass matrices.

Experimental results

Research questions

• RQ1 How can the observed hierarchy in quark and lepton masses be dynamically generated in a supergravity-based effective field theory?
• RQ2 What role do gauge singlet moduli fields play in shaping the structure of fermion mass matrices?
• RQ3 Can modular symmetry alone reproduce the phenomenologically required patterns of mass and mixing angles without explicit flavor symmetries?
• RQ4 Why do flavor-changing neutral currents from soft terms vanish identically at the Planck scale in this framework?
• RQ5 What dynamical mechanism allows the vacuum expectation values of moduli to produce the observed mass hierarchies?

Key findings

• Fermion mass matrices are generated as homogeneous functions of zero degree in moduli fields, leading to a natural suppression of large flavor-changing effects.
• The structure of the Yukawa matrices closely resembles those obtained via U(1) family symmetry, but without postulating such a symmetry.
• Flavor-changing neutral currents arising from soft terms are identically zero at the Planck scale due to the modular symmetry of the couplings.
• The framework provides a dynamical origin for the observed mass hierarchies through vacuum expectation values of moduli fields.
• The model avoids the need for fine-tuning or ad hoc flavor symmetries, offering a more fundamental explanation of flavor structure.
• The results are consistent with low-energy phenomenology and provide a compelling mechanism for flavor universality in the soft terms.